Cigarette filter hardness is important to the consumer and can also affect the efficiency of cigarette manufacturing. To choose the optimum tow item for specific applications, it is important to be able to estimate hardness for a range of tow items and rod dimensions. Empirical models are available which are suitable for tow selection, but do not provide the mechanistic insight required for filter tow research. Previously, a relationship was described which relates the filter rod dimensions and tow parameters to the radial force exerted by the tow against the plugwrap. That relationship, referred to as the radial compression factor, models the interaction between longitudinal extension and radial expansion of bloomed tow. The radial compression factor was shown to be useful for estimating capability limits and rod weight variability. In the work reported here, the radial compression factor is related to filter hardness by application of Hooke's law. For a given tow item, a single-parameter force constant enables unbiased estimation of hardness as a function of tow weight and rod circumference. An empirical relationship was developed to relate the force constant to filament denier and total denier. The results show that hardness is directly related to the radial force exerted by the bloomed filter tow, and is therefore influenced by the same factors which affect other filter properties.